//--------------------------------------------------------------------------------------

//

//  File: Quaternion.h

//

//  Abstract: C++ templates for Quaternion operators and methods

//

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//------------------------------------------------------------------------------------

#ifndef _QUATERNION_H_

#define _QUATERNION_H_

#ifdef __cplusplus

#import "Vector3.h"

namespace Math

{

    template <typename Type>

    class Quaternion

    {

    public:

        // Constructors

        Quaternion();

        Quaternion(const Type &k);

        Quaternion(const Type &X, const Type &Y);

        Quaternion(const Type &T, const Type &X, const Type &Y);

        Quaternion(const Type &T, const Type &X, const Type &Y, const Type &Z);

        // Constructors to convert from rotation

        Quaternion(const Type * const r);

        Quaternion(const Type &theta, const Vector3<Type> &r);

        // Copy constructors

        Quaternion(const Quaternion<Type> &v);

        Quaternion(const Quaternion<Type> * const v);

        // Assignment operators. No conversions.

        Quaternion<Type> &operator=(const Quaternion<Type> &v);

        Quaternion<Type> &operator=(const Type * const v);

        Quaternion<Type> &operator=(const Type &k);

        // Operators

        const Quaternion<Type> operator-(Quaternion<Type> &v) const;

        const Quaternion<Type> operator+(Quaternion<Type> &v) const;

        const Quaternion<Type> operator^(Quaternion<Type> &v) const;  // Exterior Hamilton product

        const Type             operator*(Quaternion<Type> &v) const;  // Interior dot product

        const Quaternion<Type> operator-(Type &k) const;

        const Quaternion<Type> operator+(Type &k) const;

        const Quaternion<Type> operator*(Type &k) const;

        const Quaternion<Type> operator/(Type &k) const;

        Quaternion<Type> &operator+=(Type &k);

        Quaternion<Type> &operator-=(Type &k);

        Quaternion<Type> &operator*=(Type &k);

        Quaternion<Type> &operator/=(Type &k);

        // Unary Operators

        Quaternion<Type> operator+() const;

        Quaternion<Type> operator-() const;

        // Index operator with {0,1,2,3} = {t,x,y,z}

        Type &operator[](const std::size_t &i);

        const Type &operator[](const std::size_t &i) const;

        // Conversion back to rotation

        void toRotation(Type *R);

        void toRotation(Type &theta, Vector3<Type> &R);

        // Check for identity within a tolerance

        bool isIdentity(const Type &eps);

    public:

        union

        {

            Type array[4];

            struct { Type t, x, y, z; };

        }; // union

    }; // Quaternion

    double sqr(const Quaternion<double> &v);

    float  sqr(const Quaternion<float>  &v);

    double abs(const Quaternion<double> &v);

    float  abs(const Quaternion<float>  &v);

    double norm(const Quaternion<double> &v);

    float  norm(const Quaternion<float>  &v);

    double inorm(const Quaternion<double> &v);

    float  inorm(const Quaternion<float>  &v);

    double dist(const Quaternion<double> &u, const Quaternion<double> &v);

    float  dist(const Quaternion<float>  &u, const Quaternion<float>  &v);

    Quaternion<double> norml(const Quaternion<double> &v);

    Quaternion<float>  norml(const Quaternion<float>  &v);

    Quaternion<double> norml(const double &e, const Quaternion<double> &v);

    Quaternion<float>  norml(const float  &e, const Quaternion<float>  &v);

    Quaternion<double> conj(const Quaternion<double> &v);

    Quaternion<float>  conj(const Quaternion<float>  &v);

    Quaternion<double> diff(const Quaternion<double> &u, const Quaternion<double> &v);

    Quaternion<float>  diff(const Quaternion<float>  &u, const Quaternion<float>  &v);

} // Math

#endif

#endif